## Algebra & Number Theory

### Algebraic de Rham theory for weakly holomorphic modular forms of level one

#### Abstract

We establish an Eichler–Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. This leads to formulae for the periods and quasiperiods of modular forms.

#### Article information

Source
Algebra Number Theory, Volume 12, Number 3 (2018), 723-750.

Dates
Revised: 22 December 2017
Accepted: 22 January 2018
First available in Project Euclid: 28 July 2018

https://projecteuclid.org/euclid.ant/1532743369

Digital Object Identifier
doi:10.2140/ant.2018.12.723

Mathematical Reviews number (MathSciNet)
MR3815311

Zentralblatt MATH identifier
06890766

#### Citation

Brown, Francis; Hain, Richard. Algebraic de Rham theory for weakly holomorphic modular forms of level one. Algebra Number Theory 12 (2018), no. 3, 723--750. doi:10.2140/ant.2018.12.723. https://projecteuclid.org/euclid.ant/1532743369

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